After asking the muscular athletes how they were coping with the heat, she told them, with a smile: “You guys look very fit.”

The Prince and the Duchess also met 16 bikini-clad members of Australia’s women’s hockey team, who waded out of a recovery pool to greet them.

With sweat breaking out on his forehead, the Prince was asked if he was hot in his suit and tie, and told 24-year-old Rachael Lynch: “I’m very jealous of you in the pool.”

Miss Lynch, from Melbourne, said: “The Prince asked us when our first game was and he wanted to know if we got hacked around the shins. We were hoping he would come in and join us!”

In the weightlifting hall the Royal party met British gold medal hopeful Zoe Smith, 16, who is competing in the 58kg weight division.

Miss Smith, who was practising with a 35kg bar, well below her personal best of 86kg, invited the Prince to “be my guest” and have a go at lifting it.

“Not with my back I’m not,” he replied.

The Prince and the Duchess were also introduced to Danielle Brown, 26, who won an archery gold medal at the 2008 Beijing Paralympics and who will become the first English Paralympian to compete in an able-bodied event at a Commonwealth Games.

The Prince is in New Delhi to represent the Queen, who is head of the Commonwealth.